Using grazing incidence X-ray diffraction, perylene crystallites grown on thin highly oriented poly(tetrafluoroethylene) (PTFE) films on silicon substrates have been investigated. All the perylene crystallites are found to orient with the ab plane of the monoclinic unit cell parallel to the substrate. The scattering data is interpreted as a trimodal texture of oriented perylene crystallites, induced by interactions between the perylene molecules and the oriented PTFE substrate. Three families of biaxial orientations are seen, with the <h10 > axes (h = 1, 2, or 3) parallel to the PTFE alignment, all having the ab-plane parallel to the substrate. About 92% of the scattered intensity corresponds to a population with <110 > highly parallel to <001 >(PTFE).